The bag does inflate slightly under normal use, but often
imperceptibly so. Many people would expect the bag to nearly fully
inflate, so the disclaimer is to help ward off panic during an
The purpose of the bag is as an oxygen reservoir. The flow of oxygen
to the mask is in a slow continuous stream, but your breathing is more
erratic -- you're only inhaling some of the time, and at different
speeds. The bag is fitted with a one-way valve which stores oxygen in
the bag when you're exhaling, and provides oxygen to you when
inhaling. In a way, it's a personal "buffer zone" that compensates for
each passenger's respiratory rate.
Using a reservoir bag in this manner allows for a much slower oxygen
flow, which is important when you're providing oxygen to an entire
plane full of people!
Reservoir bags are also commonly used on medical breathing apparatus,
for administering oxygen and/or anesthetics:
Search terms used: "may not inflate" oxygen, oxygen mask reservoir